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ON PAIRS OF GOLDBACH–LINNIK EQUATIONS
Part of:
Additive number theory; partitions
Published online by Cambridge University Press: 19 October 2016
Abstract
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In this paper, we show that every pair of large positive even integers can be represented in the form of a pair of Goldbach–Linnik equations, that is, linear equations in two primes and $k$ powers of two. In particular,
$k=34$ powers of two suffice, in general, and
$k=18$ under the generalised Riemann hypothesis. Our result sharpens the number of powers of two in previous results, which gave
$k=62$, in general, and
$k=31$ under the generalised Riemann hypothesis.
MSC classification
- Type
- Research Article
- Information
- Copyright
- © 2016 Australian Mathematical Publishing Association Inc.
Footnotes
This work is supported by the National Natural Science Foundation of China (Grant Nos. 11426048 and 11301372), Specialised Research Fund for the Doctoral Program of Higher Education (Grant No. 20130032120073) and Independent Innovation Foundation of Tianjin University (Grant Nos 190-0903061029 and 190-0903062072).
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